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Making use of the well-known phase space reduction in the lowest Landaulevel(LLL), we show that the Laughlin wave function for the $\nu = {1\over m}$case can be obtained exactly as a coherent state representation of an onedimensional $(1D)$ wave function. The $1D$ system consists of $m$ copies offree fermions associated with each of the $N$ electrons, confined in a commonharmonic well potential. Interestingly, the condition for this exactcorrespondence is found to incorporate Jain's parton picture. We argue that,this correspondence between the free fermions and quantum Hall effect is due tothe mapping of the $1D$ system under consideration, to the Gaussian unitaryensemble in the random matrix theory.Comment: 7 pages, Latex , no figure

Laughlin wave function and one-dimensional free fermions